[tex]\text{The slope-intercept form}\ y=mx+b\\\\m=\dfrac{y_2-y_1}{x_2-x_1}\\\\\text{We have the points}\ (1, -3)\ \text{and}\ (3,10).\ Substitute:\\\\m=\dfrac{1-(-3)}{3-1}=\dfrac{4}{2}=2\to y=2x+b\\\\\text{substitute the coordinates of the point (3, 1) to the equation:}\\\\1=2(3)+b\\1=6+b\qquad|-6\\\\-5=b\to b=-5\\\\Answer:\ \boxed{D.\ y=2x-5}[/tex]
